Reds not true to life

When taking a picture of red roses in my garden, the camera screen colour is very different from what I'm seeing, even though the roses are shown a sort of red. Furthermore, where the sun is shining on the rose petals and making certain parts of them much brighter, the resulting highlights are virtually whitened out.

Is there something wrong with the camera, or do I merely need to find the best setting? I've tried several modes, but found the same problem always.